This invention relates to shim coils for magnetic resonance applications. In particular, the invention is directed to the design of asymmetric shim coils for magnetic resonance imaging machines.
In magnetic resonance imaging (MRI) applications, a patient is placed in a strong and homogeneous static magnetic field, causing the otherwise randomly oriented magnetic moments of the protons, in water molecules within the body, to precess around the direction of the applied field. The part of the body in the homogeneous region of the magnet is then irradiated with radio-frequency (RF) energy, causing some of the protons to change their spin orientation. The net magnetization of the spin ensemble is nutated away from the direction of the applied static magnetic field by the applied RF energy. The component of this net magnetization orthogonal to the direction of the applied static magnetic field acts to induce measurable signal in a receiver coil tuned to the frequency of precession. This is the magnetic resonance (MR) signal. Most importantly, the frequency at which protons precess around the applied static field depends on the background magnetic field. Since this is designed to vary at each point in the sample in an imaging experiment, it follows that the frequency of the MR signal likewise depends on location. The signal is therefore spatially encoded, and this fact is used to construct the final image.
In practice, construction tolerances mean that MR magnets do not generate perfectly homogeneous fields over the DSV (the specified Diameter-Sensitive Volume; also referred to herein as the xe2x80x9cpredetermined shimming volumexe2x80x9d) and therefore require some adjustment of the field purity which is achieved by shimming. In addition, the presence of the patient""s body perturbs the strong magnetic field slightly, and so shim coils are used to correct the field, to give the best possible final image. The field within the DSV is typically represented in terms of spherical harmonics, and so impurities in the field are analyzed in terms of the coefficients of an expansion in these harmonics. Correction coils are therefore designed to produce a particular magnetic field shape that can be added to the background magnetic field, so as to cancel the effect of one or more of these spherical harmonics. Many of these coils may be present in a particular MRI device, and each may have its own power supply to produce the required current flow. Zonal shim coils are those that possess complete azimuthal symmetry; that is, have the same current density around the periphery of the cylinder for each point along its length.
The main design task associated with these correction coils is to determine the precise windings on the coil that will produce the desired magnetic field within the coil. One method, due to Turner (1986, A target field approach to optimal coil design, J. Phys. D: Appl. Phys. 19, 147-151; U.S. Pat. No. 4,896,129), is to specify a desired target field inside the cylinder, at some radius less than the coil radius. Fourier transform methods are then used to find the current density on the surface of the coil required to give the desired target field. This method has been widely used, and is successful in applications, but suffers from three significant drawbacks. Firstly, the method does not allow the length of the coil to be specified in advance. Secondly, so that the Fourier-transform technique can be applied to finite length coils, the target fields must be moderated or smoothed in some way, so that the Fourier transforms converge, and this can introduce unnecessary errors and complications. Thirdly, because the coils in this approach are not given an explicit length, there is no straightforward way of using this method to design asymmetrically locates target fields in a coil of finite length.
An alternative method for the design of coils of finite length is the stochastic optimization approach pioneered by Crozier and Doddrell (1993, Gradient-coil design by simulated annealing, J. Magn. Reson. A 103, 354-357). This approach seeks to produce a desired field in the DSV using optimization methods to adjust the location of certain loops of wire and the current flowing in those loops. The method is very robust, since it uses simulated annealing as its optimization strategy, and it can incorporate other constraints in a straightforward manner by means of a Lagrange-multiplier technique. Coils of genuinely finite length are accounted for without approximation by this technique, and it therefore has distinct advantages over the target field method (and alternative methods based on finite-elements). Since it relies on a stochastic optimization strategy, it can even cope with discontinuous objective functions, and so can accommodate adding or removing loops of wire during the optimization process. The method has the drawback that the stochastic optimization technique can take many iterations to converge, and so can be expensive of computer time.
It is an object of this invention to provide coil structures that generate desired fields within certain specific, and asymmetric portions of the overall coil.
It is a further object of the present invention to provide a general systematic method for producing a desired zonal magnetic field within the coil, but using a technique that retains the simplicity of a direct analytical approach. In connection with this object, the desired zonal magnetic field can be located symmetrically or asymmetrically with respect to the overall geometry of the coil.
In one broad form, the invention provides a method for the design of symmetric and asymmetric zonal shim coils of a MR device. The method uses Fourier-series to represent the magnetic field inside and outside a specified volume. Typically, the volume is a cylindrical volume of length 2 L and radius a within the MR device. The current density on the cylinder is also represented using Fourier series. This approximate technique ignores xe2x80x9cend effectsxe2x80x9d near the two ends of the coil, but gives an accurate representation of the fields and currents inside the coil, away from the ends.
Any desired field can be specified in advance on the cylinder""s radius, over some portion (e.g., a non-symmetric portion) pL less than z less than qL of the coil""s length (xe2x88x921 less than p less than q less than 1). Periodic extension of the field is used in a way that guarantees the continuity of the field, and therefore gives good convergence of the Fourier series.
For example, the desired target field in an asymmetric position of the cylindrical volume is represented as a periodic function of period equal to twice the length of the coil (i.e. 4 L). The extended periodic target field can be represented as an even periodic extension about an end of the coil. All that is required is to calculate the Fourier coefficients associated with the specified desired field, and from these, the current density on the coil and the magnetic field components then follow. In another broad form, the invention provides asymmetric zonal shim coils for MR systems. Asymmetric shim coils can be used in conventional MR systems or in the newly developed asymmetric magnets, such as the magnets of U.S. Pat. No. 6,140,900.
Thus, in accordance with certain of its aspects, the invention provides a zonal shim coil (e.g., a member of a shim set) having (i) a longitudinal axis (e.g., the z-axis) and (ii) a predetermined shimming volume (the dsv), and comprising a plurality of current-carrying windings which surround and are spaced along the longitudinal axis, said coil producing a magnetic field, the longitudinal component of which is given by:             B      z        ⁡          (              r        ,        θ            )        =            ∑              n        =        0            ∞        ⁢                  r        n            ⁡              (                              a            n0                    ⁢                                    P              n0                        ⁡                          (                              cos                ⁢                                  xe2x80x83                                ⁢                θ                            )                                      )            
where an0 are the amplitudes of the zonal harmonics, Pn0(cos xcex8) are Legendre polynomials, n is the order of the polynomial, and r and xcex8 are radial and azimuthal coordinates, respectively;
wherein:
(i) the coil generates at least one predetermined zonal harmonic whose order (nxe2x80x2) is greater than or equal to 2, e.g., the coil can generate a single harmonic, e.g., nxe2x80x2 can equal, for example, 2, 3, 4, 5, 6, 7, or 8, or, if desired, the coil can simultaneously generate more than one harmonic, e.g., nxe2x80x2 can equal 2 and 4 or can equal 3 and 5;
(ii) the coil has first and second ends which define a length 2 L; and
(iii) the predetermined shimming volume extends along the longitudinal axis from z=pL to z=qL, where
(a) xe2x88x921 less than p less than q less than 1;
(b) |p|xe2x89xa0|q| (i.e., the predetermined shimming volume is located asymmetrically with respect to the overall geometry of the coil); and
(c) z=0 is midway between the first and second ends of the coil.
Preferably, all of the coils in the shim set are of the above type.
In the case of zonal shim coils used for high resolution spectroscopy, i.e., NMR, qxe2x88x92p is preferably greater than or equal to 0.01 and most preferably greater than or equal to 0.05. In the case of zonal shim coils used for clinical imaging, i.e., MRI, qxe2x88x92p is preferably greater than or equal to 0.05 and most preferably greater than or equal to 0.5.
In accordance with certain preferred embodiments of the invention, the zonal shim coil generates a single predetermined zonal harmonic, the predetermined shimming volume defines a midpoint M along the longitudinal axis, the predetermined shimming volume has a characteristic radius R given by:
R=(qxe2x88x92p)L/2 when qxe2x88x92p less than 1,
and by:
R=(qxe2x88x92p)L/3 when qxe2x88x92pxe2x89xa71,
and the zonal shim coil has a purity (Pxe2x80x2) which is less than or equal to 0.2, where:       P    xe2x80x2    =            (                                    ∑            0                                          n                xe2x80x2                            -              1                                ⁢                                    "LeftBracketingBar"                              a                n0                            "RightBracketingBar"                        ⁢                          R              n                                      +                              ∑                                          n                xe2x80x2                            +              1                                                      n                xe2x80x2                            +              6                                ⁢                                    "LeftBracketingBar"                              a                n0                            "RightBracketingBar"                        ⁢                          R              n                                          )        /                  (                              "LeftBracketingBar"                          a                                                n                  xe2x80x2                                ⁢                0                                      "RightBracketingBar"                    ⁢                      R                          n              xe2x80x2                                      )            .      
Most preferably, Pxe2x80x2 is less than or equal to 0.05.
In certain specific applications of the invention, the zonal shim coil has the following characteristics:
(i) nxe2x80x2=2 or 3;
(ii) qxe2x88x92pxe2x89xa70.7;
(iii) 2 Lxe2x89xa61.4 meters; and
(iv) Pxe2x80x2xe2x89xa60.1;
while in other specific applications, it has the following characteristics:
(i) nxe2x80x2=4,5,6,7, or 8;
(ii) qxe2x88x92pxe2x89xa70.7;
(iii) 2 Lxe2x89xa61.4 meters; and
(iv) Pxe2x80x2xe2x89xa60.2.
For clinical imaging applications of the invention, either |p| or |q| is preferably greater than or equal to 0.7.
In accordance with certain others of its aspects, the invention provides a method for designing a zonal shim coil for a magnetic resonance system, said shim coil extending from xe2x88x92L to +L along a longitudinal axis which lies along the z-axis of a three dimensional coordinate system, said method comprising:
(a) selecting a cylindrical surface having a radius r=a for calculating current densities for the shim coil (the xe2x80x9cr=a surfacexe2x80x9d), said surface surrounding the longitudinal axis, extending from xe2x88x92L to +3 L, and having a first region which extends from xe2x88x92L to +L and a second region which extends from +L to +3 L;
(b) for the first region, selecting a set of desired values for the longitudinal component of the magnetic field (Bz(axe2x88x92,z)) to be produced by the shim coil at locations which are (i) spaced along the longitudinal axis and (ii) on the internal side of the r=a surface (r=axe2x88x92) wherein:
(1) the first region consists of first, second, and third subregions which extend in order along the longitudinal axis from z=xe2x88x92L to z=+L, with the first subregion extending from z=xe2x88x92L to z=pL, the second subregion extending from z=pL to z=qL, and the third subregion extending from z=qL to z=+L, where:
xe2x88x921 less than p less than q less than 1;
(2) the desired values for the longitudinal component of the magnetic field are defined by a preselected zonal harmonic for the second subregion; and
(3) the desired values for the magnetic field for the first and third subregions are selected to satisfy the following equation:             ∫              -        L            L        ⁢                            B          z                ⁡                  (                                    a              -                        ,            z                    )                    ⁢              ⅆ        z              =  0
(c) for the second region, selecting a set of calculation values for locations which are (i) spaced along the longitudinal axis and (ii) on the internal side of the r=a surface (r=axe2x88x92) wherein said set of calculation values are the reflection about z=+L of the set of desired values of the first region; and
(d) determining a current density distribution js(z) for the shim coil for the first region by:
(1) calculating coefficients for a Fourier series expansion for the longitudinal magnetic field from the set of selected desired values for the first region and the set of selected calculation values for the second region; and
(2) calculating the current density distribution by simultaneously solving the equations (1) to (3) set forth below in combination with the equation B=xe2x88x92∇"psgr" using the Fourier coefficients calculated in step (d)(1).
The method preferably also includes the additional step of generating discrete current carrying windings for the shim coil from the current density distribution js(z) by:
(1) integrating |js(z)| with respect to z over the range from xe2x88x92L to +L to determine a total current J;
(2) selecting a number of current carrying windings N;
(3) determining a current per winding value I=J/N;
(4) determining a set of js(z) blocks over the range from xe2x88x92L to +L such that the integral of |js(z)| over each block equals I; and
(5) for all blocks having a net polarity for js(z) over the block, placing a winding at the center of the block, the direction of the current in the winding corresponding to said net polarity.
The method can be used for a symmetrically located second subregion in which case |p|=|q| or for an asymmetrically located second subregion in which case |p|xe2x89xa0|q|.
Further details of the invention are presented below.